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A Simple Proof Of Bell's Theorem 
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#19
Jul2810, 01:25 AM

P: 1,414

Of course, there's the possibility that OPTICAL Bell tests have nothing to do with OPTICS (per DrChinese et al.), but I think that that's just clutching at straws. 


#20
Jul2810, 09:14 AM

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PF Gold
P: 5,385




#21
Jul2810, 10:41 AM

Sci Advisor
P: 8,470

And again, do a little selfreflection, do you really believe that as an amateur who has made no formal study of physics, you really have a rational basis for being confident that I (and DrChinese and RUTA and others) are wrong about the typical beliefs of physicists? You have cited only two papers with significant overlap in authorship, do you think that's enough to justify the conclusion that a significant fraction of the physics community disagrees with Bell's conclusions? Given how strongly you seem to want Bell's theorem to be wrong, do you think you are immune to effects like confirmation bias, not to mention the DunningKruger effect? So, sorry about the mistake, but there was really no need to accuse me of obfuscation since my confusion was genuine. And in my defense, I don't think there is perfect uniformity in how different authors use the phrase "coincidence rate", for example this page says: Anyway, with the understanding that we're looking at the coincidence rate with polarizers at angles a and b expressed as a fraction of the rate of detection with no polarizers in place, I agree that your setupwhere photons going towards A meet no polarizers, while photons going towards B encounter two polarizers at angles a and b in successionwill indeed yield the same coincidence rate as with the normal setup where the photon going towards B encounters a polarizer at angle b while the photon going towards A encounters a polarizer at angle a. However, the crucial point is that your setup does not meet the experimental conditions specified by Bell, which include the fact that there must be a spacelike separation between the random choice of angle a for the polarizer that photon #1 encounters and the event of photon #2 encountering the other polarizer at angle b. This spacelike separation is crucial, because in a local universe it means there can be no causal influence between the choice of angle a and the event of the photon either passing through or being reflected by b. This is why it would be quite possible to reproduce the 0.5 cos^2 (ab) relationship you describe using classical optics (you'd just need a detector that gave a binary yes/no result depending on whether the light that reached it was above a certain threshold), but it would be impossible to reproduce the 0.5 cos^2 (ab) relationship in a classical optics experiment that actually satisfied Bell's experimental conditions, including the part about the spacelike separation. And this is why the following argument is just a giant strawman: 


#22
Jul2910, 01:38 PM

Sci Advisor
PF Gold
P: 5,385

OK, how about this one:
1. Take 2 classical sets of binary observables that are uncorrelated. Say, 2 stacks of 100 coins which were randomly flipped to H or T and then paired. One stack is Alice, the other is Bob. About 50 pairs will match (ideal case), about 50 will mismatch, so 0 net correlation. 2. Find a 3rd set which has this property: it is equally correlated to Alice and Bob (in the ideal case, ignore if off by 1). There should be such a set. 3. What is the correlation of that set to Alice and Bob? Classically, it MUST be exactly .5 (within some confidence level related to sample size). Because the midpoint of 100% matches and 50% matches is 75% matches, which is a correlation of 50% (75% matches less 25% mismatches). 4. However, in the quantum version of this (PDC Type I entangled photon pairs), the correlation is more like .7 (85% matches less 15% mismatches). Imagine Alice and Bob at 0 and 45 degrees. They will not be correlated at all. But their midpoint, 22.5 degrees, is 70% correlated (85% matched) to Alice AND 70% correlated (85% matched) to Bob. That's impossible with any classical set; ergo there is no classical set. Or look at it from the other perspective: 1. I have 100 tossed coins (data values for a set at 22.5 degrees). Is it possible to obtain 2 different sets by turning over 15 coins from each set so that those new sets (Alice and Bob) are maximally different? Certainly, but how different can they be? Classically and quantum mechancially, you get different answers! 2. Classically, you will have sets that are no more than 30% different (15 changed in Alice + 15 changed in Bob out of 100 original). 3. In the QM world: When Alice is 0 degrees and Bob is 45 degrees (the farthest points where they are 15% different than the starting point of 22.5 degrees), well, those points are completely uncorrelated with each other (i.e. 50% different). Ergo, there are no classical datasets which have this simple observed property: 15%+15%=50%. 


#23
Jul3010, 04:31 AM

P: 1,414




#24
Jul3010, 04:48 AM

P: 1,414

JesseM, I didn't mean to imply that you've ever deliberately obfuscated anything. I probably should have phrased my directive as a request to you to please avoid unnecessarily complicating my little 'thought illustration' if at all possible. Apparently that wasn't possible. So, that's that. Anyway, it was just meant to illustrate a couple of things. Which I'll restate, but first the setup again:
The setup is an ideal optical Bell test setup where an ideal source is emitting pairs of counterpropagating photons, entangled in polarization, at a certain rate. There are two ideal photon detectors, A and B, placed opposite each other and equidistant from the emitter, registering detections at certain, identical, rates. Between the emitter and detectors are placed two polarizers, a and b. The detection rate at A with polarizer, a, in place is 1/2 the detection rate at A without polarizer, a, in place. The detection rate at A is invariant wrt rotations of the polarizer, a. The same holds for the B side. The rate of coincidental detection is .5cos^2 ab . Now, if eg. polarizer, a, is taken from the A side and transferred to the B side, then the rate of coincidental detection will still be .5cos^2 ab . (The coincidence rate can't be greater than the maximum B side detection rate.) I think that this idealization illustrates the following: (1) It isn't just a 'coincidence', having nothing to do with optics, that the coincidence rate in the original setup is the same as the coincidence rate in the altered setup. (2) There's clearly no need for 'nonlocal communication' in the altered setup (with a photon polariscope on the B side). So, I don't think we need nonlocality to understand the correlations in the original setup. (As if assuming 'nonlocality' is any sort of understanding anyway). (3) Most importantly wrt the OP of this thread, either the altered setup is not fundamentally equivalent to the original setup, or Herbert and Bell are requiring light to behave in a way that contradicts at least two centuries of observational data (or, they're saying that Malus Law, as it applies to quantum polariscopic setups, is, per se, implying nonlocality). Of course, one could maintain that the two setups are so different that in the original one (an idealization of the archetypal optical Bell test setup) with a polarizer on each side, some unknown field (or whatever) has been conjured from the depths of reality to enable the counterpropagating photons (or whatever) to communicate instantaneously (or, conveniently, as faster than light speed as the setup requires). But I find it difficult to imagine how the mere placement of a polarizer could have such, er, power, and think that a more plausible hypothesis is that people who think that violations of BI's (such as Herbert's 'simplest' BI) imply nonlocality have simply made a logical error somewhere along the line.  Wrt what most physicists would say, it's an open empirical question. My own sampling of the physics community has lead me to believe that most physicists would say that nature is evolving according to underlying dynamical principles in accordance with the principle of local action. But of course it wasn't a large sample, and the responses were maybe not representative of the responses one might get from thousands of physicists across all the subfields in physics. Some specialties might be more predisposed to liking certain ideas or thinking in certain terms (eg., that nature is local  or nonlocal) than others.  I'm going to resist the temptation to reply to these most recent Bell threads for as long as it takes for me to catch up on my reading. I thank you, JesseM, for your detailed and sincere replies, and you and DrC and billschnieder and JenniT and my_wan and RUTA and several others for motivating me to learn more. I certainly agree that one must avoid cognitive bias and the dreaded DK syndrome. Maybe nature is nonlocal, or there are fields or media where disturbances propagate ftl. Who knows. These are open questions as far as I'm concerned. All I can say to those who think that Bell has definitively proved that nature is nonlocal is that I currently disagree with them, and, anyway, it doesn't seem to matter very much to physical science whether nature is fundamentally local or nonlocal  because these aren't questions that can be answered scientifically. To the OP, I think that Herbert's simplest Bell inequality is a valid Bell inequality, and that Herbert's interpretation of the physical meaning of its violation is not valid. But that's just my current opinion, and although that opinion is reinforced by a number of professional physicists (albeit probably not the majority of professional physicists), it might well change as my understanding of everything involved increases. What I currently understand is the categorical logic involved in BIs, and the arithmetization thereof. What I don't currently understand is what this has to do with fundamental reality. Or, to phrase it differently, I don't understand why apparently many physicists think that BI violations imply anything about fundamental reality. And, JesseM, here's a smiley for you. I was reading a recent reply of yours to RUTA in another thread. What you're saying there makes very good sense to me. That is, I agree with it. What you're saying in all of your replies, including those in this thread, makes sense to me. And, I think all your responses are well thought out and sincere. So, it's very difficult to disagree with you. However, I just don't happen to think, currently, that all of your statements, particularly pertaining to Bell, are necessarily correct. So, give me some time to read and think about this stuff and I'll get back to you  and thanks again. In the meantime, for interested readers, here are a couple of papers that you might agree are related to the Hess et al papers linked to correctly by JesseM in post #16. Bell's inequalities I: An explanation for their experimental violation Journal ref: Optics Communications 170 (1999) 5560 http://arxiv.org/ftp/quantph/papers/0101/0101087.pdf Bell's inequalities II: logical loophole in their interpretation Journal ref: Optics Communications 170 (1999) 6166 http://arxiv.org/ftp/quantph/papers/0101/0101094.pdf 


#25
Jul3010, 06:44 AM

PF Gold
P: 1,662

I don’t wanna be a "party pooper"... but somehow I wonder if this is really the whole truth... 


#26
Jul3010, 07:54 AM

PF Gold
P: 1,662

Happy reading, and remember – no one is saying that it’s proved beyond any doubt that the world is nonlocal. We are just saying that Local Realism (LR) cannot reproduce all the predictions of QM and the results of all performed EPRBell experiments so far. A little 'advice' on subjects to penetrate, while you’re reading, is the correlation on the relative angle between Alice & Bob:



#27
Jul3010, 09:35 AM

P: 1,414

But I like ruffling a few feathers now and then. And this really is my last post on this stuff for a while (I didn't feel like reading this morning). 


#28
Jul3010, 10:34 AM

PF Gold
P: 1,662

(... I’m sharpening my teeth ... ) 


#29
Jul3010, 11:32 AM

Sci Advisor
PF Gold
P: 5,385

Again, the point is that entanglement (as a state) is incompatible with local realism. 


#30
Jul3010, 01:49 PM

PF Gold
P: 1,662

DrC, I’m looking for the stuff on "remote entanglement" (particles that never was in contact), but I can’t find it on PF?



#31
Jul3010, 03:46 PM

Sci Advisor
PF Gold
P: 5,385

http://arxiv.org/abs/quantph/0609135 We report for the first time in an ancillafree process a nonlocal entanglement between two single photons which do not meet. For our experiment we derive a simple and efficient method to entangle two single photons using postselection technology. The photons are guided into an interferometer setup without the need for ancilla photons for projection into the Bellstates. After passing the output ports, the photons are analyzed using a bell state analyzer on each side. The experimental data clearly shows a nonlocal interaction between these photons, surpassing the limit set by the CHSHinequality with an Svalue of 2.54 and 24 standard deviations. http://arxiv.org/abs/0809.3991 Entanglement swapping allows to establish entanglement between independent particles that never interacted nor share any common past. This feature makes it an integral constituent of quantum repeaters. Here, we demonstrate entanglement swapping with timesynchronized independent sources with a fidelity high enough to violate a ClauserHorneShimonyHolt inequality by more than four standard deviations. The fact that both entangled pairs are created by fully independent, only electronically connected sources ensures that this technique is suitable for future longdistance quantum communication experiments as well as for novel tests on the foundations of quantum physics. http://arxiv.org/abs/quantph/0409093 We report the first experimental realization of entanglement swapping over large distances in optical fibers. Two photons separated by more than two km of optical fibers are entangled, although they never directly interacted. We use two pairs of timebin entangled qubits created in spatially separated sources and carried by photons at telecommunication wavelengths. A partial Bell state measurement is performed with one photon from each pair which projects the two remaining photons, formerly independent onto an entangled state. A visibility high enough to violate a Bell inequality is reported, after both photons have each travelled through 1.1 km of optical fiber. http://arxiv.org/abs/0911.1314 Quantum systems that have never interacted can become nonlocally correlated through a process called entanglement swapping. To characterize nonlocality in this context, we introduce local models where quantum systems that are initially uncorrelated are described by uncorrelated local variables. While a pair of maximally entangled qubits prepared in the usual way (i.e., emitted from a common source) requires a visibility close to 70% to violate a Bell inequality, we show that an entangled pair generated through entanglement swapping will already violate a Bell inequality for visibilities as low as 50% under our assumption.  Although these experiments don't show it, you can entangle photons after they are detected... and you can even entangled photons that never existed at the same time. 


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